Algorithms

pymocd ships eight detectors. SCALE and HP-MOCD are the library's own contributions; the remaining six re-implement published baselines whose authors released no code.

Overview

API	Algorithm	Objectives & engine	Solution selection	Year
scale	SCALE (Santos, in prep.)	KKM / ratio-cut bi-objective, sparse macro–micro co-evolutionary NSGA-II (near-linear, no dense kernel)	label-free SBM/MDL description length	2026
hpmocd	HP-MOCD (Santos et al.)	decomposed modularity, parallel NSGA-II	max modularity Q	2025
mmcomo	MMCoMO (Zhang et al.)	kernel k-means + ratio cut, macro/micro co-evolutionary NSGA-II	max Q (front via mmcomo_fronts)	2023
ccm	CCM (Shaik et al.)	score + fitness + modularity, NSGA-III	max Q	2021
krm	KRM (Shaik et al.)	kernel k-means + ratio cut + modularity, NSGA-III	max Q	2021
mocd_q	Shi-MOCD (Shi et al.)	decomposed modularity, PESA-II	max Q	2012
mocd_d	Shi-MOCD (Shi et al.)	decomposed modularity, PESA-II	max-min distance to random nets	2012
moga_net	MOGA-Net (Pizzuti)	community score + fitness, NSGA-II	max Q	2012

All detectors return a single crisp partition as dict[node, community]; isolated nodes are assigned community -1.

Which one should I use?

• scale — the recommended default: label-free SBM/MDL selection, near-linear time and memory.
• hpmocd — the published HP-MOCD behaviour with max-modularity selection.
• The other six — baselines for papers and benchmarks; pop_size, num_gens and rates are tunable kwargs.

SCALE

SCALE co-evolves a macro population of medoid community centres with a micro population of per-node labels over the kernel k-means / ratio-cut bi-objective, bridged by a sparse similarity carried on the graph's edges rather than a dense n×n kernel — so memory is O(n+m) and it scales to graphs the dense macro–micro baseline cannot build. The merged rank-1 front is enriched by a union refinement, and one partition is returned with no ground truth by minimising a label-free microcanonical SBM description length.

The frontier is exposed for inspection via scale_fronts.

HP-MOCD

HP-MOCD optimises decomposed modularity with a parallel NSGA-II and returns the max-Q solution from the Pareto front. The HpMocd class exposes the front itself for inspection. Published in Social Network Analysis and Mining (2025).

Citation

@article{Santos2025,
  author    = {Santos, Guilherme O. and Vieira, Lucas S. and Rossetti, Giulio and Ferreira, Carlos H. G. and Moreira, Gladston J. P.},
  title     = {A high-performance evolutionary multiobjective community detection algorithm},
  journal   = {Social Network Analysis and Mining},
  year      = {2025},
  volume    = {15},
  number    = {1},
  pages     = {110},
  doi       = {10.1007/s13278-025-01519-7},
  url       = {https://doi.org/10.1007/s13278-025-01519-7},
  issn      = {1869-5469},
  date      = {2025-11-18}
}